- #1
Calcifur
- 24
- 2
Homework Statement
Show that the equation below is an eigenfunction for the Quantum Harmonic Oscillator Hamiltonian and find its corresponding eigenvalue.
Homework Equations
u1(q)=A*q*exp((-q[itex]^{2}[/itex])/2)
The Attempt at a Solution
Ok, so I know that the Quantum Harmonic Oscillator Hamiltonian (H[itex]_{QHO}[/itex]) is :
(H[itex]_{QHO}[/itex])=[itex]\frac{1}{2}[/itex][itex]\hbar[/itex]ω(((-d^2)/(dq^2))+q^2) and I know that:
(H[itex]_{QHO}[/itex])u1(q)=Eu1(q)
but how do I show that it's an eigenfunction? Simply subbing it into the eqn doesn't appear to help.
Many thanks in advance.